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In a rectangular coordinate system, point lies on the -axis and has coordinates . If point lies on the negative -axis and the area of the triangle formed by connecting the origin, , and is , what is the -coordinate of ?
In a rectangular coordinate system, point lies on the -axis and has coordinates . If point lies on the positive -axis and the area of the triangle formed by connecting the origin, , and is , what is the -coordinate of ?
The perimeter of an isosceles right triangle is . What is the length of the hypotenuse?
In the figure shown, is inscribed in semicircle . If the length of line segment is and the length of line segment is , what is the length of arc ?
A certain right triangle has side lengths , , and , where . If the area of this triangular region is , which of the following is the value of ?
For how many ordered pairs that are solutions of the system above are and both integers?
Kara's math average went down 20% from freshman year to sophomore year. During the same time, her history average went up 8%. If her combined average in the two classes went down 8%, what is the ratio of her history average during her freshman year to her math average during freshman year?
Johan rides his bicycle to and from college every day, and the round-trip takes hours. If the radius of his bicycle's front wheel is centimeters and the wheel makes revolutions over the course of the round-trip, then which of the following is closest to Johan's average speed in kilometers per hour?
If and are two positive integers whose greatest common divisor is , what will be the remainder of , if ?
Joseph bought nails for each, hooks for each, and screws for each. Joseph bought a total of items and paid a total of . If Joseph bought twice as many nails as screws, how many hooks did he buy?
If is a prime number, is a positive integer, and , what is ?